Finescale Instabilities of the Double-Diffusive Shear Flow

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Abstract

This study examines dynamics of finescale instabilities in thermohaline–shear flows. It is shown that the
presence of the background diapycnal temperature and salinity fluxes due to double diffusion has a destabilizing
effect on the basic current. Using linear stability analysis based on the Floquet theory for the sinusoidal
basic velocity profile, the authors demonstrate that the well-known Richardson number criterion (Ri , 1/ 4)
cannot be directly applied to doubly diffusive fluids. Rigorous instabilities are predicted to occur for
Richardson numbers as high as—or even exceeding—unity. The inferences from the linear theory are supported
by the fully nonlinear numerical simulations. Since the Richardson number in the main thermocline
rarely drops below 1/ 4, whereas the observations of turbulent patches are common, the authors hypothesize
that some turbulent mixing events can be attributed to the finescale instabilities associated with double diffusive
processes.

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